Modelling count and growth data with many zeros

We discuss the problem of modelling survival/mortality and growth data that are skewed with excess zeros. This type of data is a common occurrence in biological and environmental studies. The method presented here allows us to utilize both the survival/mortality and growth data when both data sets contain a large proportion of zeros. The method consists of four stages. Firstly the original data is divided into two sets; one contains all the surviving organisms and the other all of the mortalities. Secondly we calculate the actual growth of the surviving organisms and of the mortalities. Thirdly we count the number of surviving organisms for which growth has occurred and the number where no growth occurred, and the same count procedure is carried out on the mortalities. Next we model the survival/mortality data and growth/no growth data using logistic regression, and separately model the growth data using an ordinary regression. Finally we combine the three models to estimate the expected growth for a specific set of values of the explanatory variables. If we used another statistical method that did not involve the dead mussels or the ones with no growth, some of the information provided by these mussels would be lost. However, using the method we propose, all of the data collected are used to achieve an optimal estimation of the mussel growth. A case study of survival and growth of blue mussels (Mytilus galloprovincialis) and ribbed mussels (Aulacomya atra maoriana) trans-located from their natural distribution to different depths and sites along the axis of Doubtful Sound, New Zealand, is used for illustration.